Millikan's oil-drop experiment is one of the classic experiments from the history of physics. Due to its content (the determination of the elementary charge) it is also among those experiments that are frequently used and discussed in teaching situations. Disappointingly, a review of the educational literature on this experiment reveals that its implementation in teaching situations is not especially successful. Using a collaborative approach, we have attempted to develop an understanding of the difficulties that students encounter with this experiment. In our approach, apart from evaluating students' lab reports, we used questionnaires and semi-structured interviews. Additionally, we have used the historical development of the oil-drop experiment as a resource for restructuring the educational use of the experiment, and we have attempted to develop a more thorough understanding of the experiment through an analysis of the data generated in the experiment and its mathematical treatment. As a result, we suggest a different use of the apparatus that appears to result in less frustration of the students as well as a better understanding of the experiment and its difficulties by the students. (Contains 7 figures and 5 footnotes.)